Question

A parallelogram has an area of 120 square units. Its perimeter is between 40 and 50 units. List two possible dimensions for the parallelogram.

Answer 1

The dimensions are:

10 units and 12 units

10 units and 14 units

Explanation:

∵ The area of the parallelogram is 120 units²

∵ 40 < perimeter of it < 50

∵ Perimeter of it = 2(b1 + b2)

∴ 40 < 2(b1 + b2) < 50 ⇒ ÷ 2

∴ 20 < b1 + b2 < 25

∴ b1 + b2 = 21 , 22 , 23 , 24

* We can chose any sum of them

∵ The area of the parallelogram = b1 × h1 = b2 × h2

∵ b1 × h1 = 120

∴ We can chose b1 = 10 so h1 = 12 ⇒ b2 = 11 , 12 , 13 , 14

Or we can chose b1 = 12 so h1 = 10 ⇒ b2 = 9 , 10 , 11

∴ We can chose any two dimensions above